logo

SCIENCE CHINA Information Sciences, Volume 59, Issue 3: 032106(2016) https://doi.org/10.1007/s11432-015-5305-y

Linear complexity problems of level sequences of Euler quotients and their related binary sequences

More info
  • ReceivedOct 22, 2014
  • AcceptedJan 8, 2015
  • PublishedJul 13, 2015

Abstract

There is no abstract available for this article.


References

[1] Agoh T, Dilcher K, Skula L. J Number Theory, 1997, 66: 29-50 CrossRef Google Scholar

[2] Sha M. Period Math Hung, 2015, doi: 10-3 Google Scholar

[3] Bourgain J, Ford K, Konyagin S, et al. Michigan Math J, 2010, 59: 313-328 CrossRef Google Scholar

[4] Chang M C. Acta Arith, 2012, 152: 23-38 CrossRef Google Scholar

[5] Chen Z X, Ostafe A, Winterhof A. Structure of pseudorandom numbers derived from Fermat quotients. In: Proceedings of the 3rd International Conference on Arithmetic of Finite Fields. Berlin: Springer-Verlag, 2010. 73--85. Google Scholar

[6] Chen Z X, Winterhof A. Int J Number Theory, 2012, 8: 631-641 CrossRef Google Scholar

[7] Chen Z X, Winterhof A. Contemp Math, 2012, 579: 67-73 CrossRef Google Scholar

[8] Chen Z X, Winterhof A. SIAM J Discr Math, 2014, 28: 1-7 CrossRef Google Scholar

[9] Ernvall R, Mets{ä}nkyl{ä} T. Math Comput, 1997, 66: 1353-1365 CrossRef Google Scholar

[10] Gómez-Pérez D, Winterhof A. Period Math Hungar, 2012, 64: 161-168 CrossRef Google Scholar

[11] Ostafe A, Shparlinski I E. SIAM J Discr Math, 2011, 25: 50-71 CrossRef Google Scholar

[12] Shparlinski I E. Quart J Math, 2011, 62: 1031-1043 CrossRef Google Scholar

[13] Shparlinski I E. Bull Aust Math Soc, 2011, 83: 456-462 CrossRef Google Scholar

[14] Shparlinski I E. Proc Amer Math Soc, 2012, 140: 1199-1206 CrossRef Google Scholar

[15] Shparlinski I E. Bull Lond Math Soc, 2011, 43: 1228-1238 CrossRef Google Scholar

[16] Shparlinski I E, Winterhof A. Finite Fields Appl, 2013, 19: 93-104 CrossRef Google Scholar

[17] Fan S Q, Han W B. Sci China Ser A-Math, 2003, 46: 516-524 Google Scholar

[18] Fan S Q, Han W B. IEEE Trans Inf Theory, 2003, 49: 1553-1557 CrossRef Google Scholar

[19] Zheng Q X, Qi W F. IEEE Trans Inf Theory, 2010, 56: 555-563 CrossRef Google Scholar

[20] Zheng Q X, Qi W F, Tian T. IEEE Trans Inf Theory, 2013, 59: 680-690 CrossRef Google Scholar

[21] Zhu X Y, Qi W F. Finite Fields Appl, 2005, 11: 30-44 CrossRef Google Scholar

[22] Zhu X Y, Qi W F. II. Finite Fields Appl, 2007, 13: 230-248 CrossRef Google Scholar

[23] Qi W F, Zhou J J. Sci China Ser A-Math, 1997, 40: 606-611 CrossRef Google Scholar

[24] Tian T, Qi W F. Finite Fields Appl, 2009, 15: 214-235 CrossRef Google Scholar

[25] Aly H, Winterhof A. Cryptogr Commun, 2011, 3: 165-174 CrossRef Google Scholar

[26] Chen Z X. Sci China Inf Sci, 2014, 57: 112109-174 Google Scholar

[27] Chen Z X, Du X N. Des Codes Cryptogr, 2013, 67: 317-323 CrossRef Google Scholar

[28] Chen Z X, Du X N, Marzouk R. Appl Algebra Eng Commun Comput, 2015, doi: 10-4 Google Scholar

[29] Chen Z X, Gómez-Pérez D. Linear complexity of binary sequences derived from polynomial quotients. In: Proceedings of the 7th International Conference on Sequences and Their Application. Berlin: Springer-Verlag, 2012. 181--189. Google Scholar

[30] Chen Z X, Hu L, Du X N. Chin Commun, 2012, 9: 105-108 Google Scholar

[31] Chen Z X, Niu Z H, Wu C H. Sci China Inf Sci, 2015, 58: 092107-108 Google Scholar

[32] Du X N, Chen Z X, Hu L. Inform Process Lett, 2012, 112: 604-609 CrossRef Google Scholar

[33] Du X N, Klapper A, Chen Z X. Inform Process Lett, 2012, 112: 233-237 CrossRef Google Scholar

[34] Wu C H, Chen Z X, Du X N. IEICE Trans Fund Electron Commun Comput Sci, 2012, E95-A: 1197-1199 CrossRef Google Scholar

[35] Cusick T W, Ding C S, Renvall A. Stream Ciphers and Number Theory. Amsterdam: North-Holland Publishing Co., 1998. Google Scholar

[36] Lidl R, Niederreiter H. Finite Fields. 2nd ed. Cambridge: Cambridge University Press, 1997. Google Scholar

[37] Meid W. How many bits have to be changed to decrease the linear complexity? Des Codes Cryptogr, 2004, 33: 109--122. Google Scholar

[38] Stamp M, Martin C F. IEEE Trans Inf Theory, 1993, 39: 1398-1401 CrossRef Google Scholar

[39] Ding C S, Xiao G Z, Shan W J. The Stability Theory of Stream Ciphers. Berlin: Springer-Verlag, 1991. Google Scholar

[40] Massey J L. IEEE Trans Inf Theory, 1969, 15: 122-127 CrossRef Google Scholar

[41] Leeb W. Linear complexity of extensions of Fermat quotients. In: Proceedings of the 83rd Workshop on General Algebra and the 27th Conference of Young Algebraists, Novi Sad, 2012. Google Scholar

[42] Blackburn S R, Etzion T, Paterson K G. J Comb Theory Ser A, 1996, 76: 55-82 CrossRef Google Scholar

[43] Nathanson M B. Elementary Methods in Number Theory. New York: Springer-Verlag, 2000. Google Scholar

Copyright 2019 Science China Press Co., Ltd. 《中国科学》杂志社有限责任公司 版权所有

京ICP备18024590号-1